Detecting quantum non-Gaussianity of noisy Schrödinger cat states

Palma, Mattia L; Stammers, Jimmy; Genoni, Marco G.; Tufarelli, Tommaso; Olivares, Stefano; Kim, M S; Paris, Matteo G. A.

doi:10.1088/0031-8949/2014/t160/014035

Cited by 5 publications

(8 citation statements)

References 14 publications

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“…on the contrary, criterion (2) uses only the most common method of photon autocorrelation measurement and criterion (3) employs only detectors distinguishing no photons, single photon and more than one photon. Compared to [32], this largely relaxes the conditions for conclusive and faithful photon number resolution. Simultaneously, they are more demanding on the quality of prepared states than the nonclassicality criterion [16,22], rejecting all classical waves.…”

Section: Quantum Non-gaussianitymentioning

confidence: 98%

“…However, the negativity always vanishes for 3 dB of loss, which is too challenging for many experimental platforms in optics [1]. For large losses, certification of the quantum non-Gaussianity employing the Wigner function becomes less demanding on the losses if a constraint on the mean number of photons is involved in the criterion [32]. However, this requires either quantum tomography using homodyne detection, challenging for many atomic and solid-state experiments or, ideally, direct detection resolving all the photon numbers to determine the mean number of photons without systematic errors.…”

Section: Quantum Non-gaussianitymentioning

confidence: 99%

“…We provide only the approximate formulas for P s and P e appropriate for states with |α| 2 1 and n 1. Under these assumptions, they get simplified to P s = η 2 P e = η (η − 1)g 2 + 2ηγκ 2 g 4 |α| 2 + ηn, (32) for both the considered noise. Fig.…”

Section: Appendix: Effects Of the Noisementioning

confidence: 99%

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Direct detection of quantum non-Gaussian light from a dispersively coupled single atom

Verma

Lachman

Filip

2022

Quantum

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Many applications in quantum communication, sensing and computation need provably quantum non-Gaussian light. Recently such light, witnessed by a negative Wigner function, has been estimated using homodyne tomography from a single atom dispersively coupled to a high-finesse cavity. This opens an investigation of quantum non-Gaussian light for many experiments with atoms and solid-state emitters. However, at their early stage, an atom or emitter in a cavity system with different channels to the environment and additional noise are insufficient to produce negative Wigner functions. Moreover, homodyne detection is frequently challenging for such experiments. We analyse these issues and prove that such cavities can be used to emit quantum non-Gaussian light employing single-photon detection in the Hanbury Brown and Twiss configuration and quantum non-Gaussianity criteria suitable for this measurement. We investigate in detail cases of considerable cavity leakage when the negativity of the Wigner function disappears completely. Advantageously, quantum non-Gaussian light can be still conclusively proven for a large set of the cavity parameters at the cost of overall measurement time, even if noise is present.

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Section: Quantum Non-gaussianitymentioning

confidence: 98%

Section: Quantum Non-gaussianitymentioning

confidence: 99%

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Direct detection of quantum non-Gaussian light from a dispersively coupled single atom

Verma

Lachman

Filip

2022

Quantum

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“…Determining whether a given state ρ belongs to the convex hull C of the Gaussian set is a difficult problem [15][16][17][18] . Then, there comes the need to find criteria to certify that ρ cannot be written in the form (21).…”

Section: Characterization Of Gaussian-to-gaussian Mapsmentioning

confidence: 99%

Normal form decomposition for Gaussian-to-Gaussian superoperators

Palma

Mari

Giovannetti

et al. 2015

Journal of Mathematical Physics

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In this paper we explore the set of linear maps sending the set of quantum Gaussian states into itself. These maps are in general not positive, a feature which can be exploited as a test to check whether a given quantum state belongs to the convex hull of Gaussian states (if one of the considered maps sends it into a non positive operator, the above state is certified not to belong to the set). Generalizing a result known to be valid under the assumption of complete positivity, we provide a characterization of these Gaussian-to-Gaussian (not necessarily positive) superoperators in terms of their action on the characteristic function of the inputs. For the special case of one-mode mappings we also show that any Gaussian-to-Gaussian superoperator can be expressed as a concatenation of a phase-space dilatation, followed by the action of a completely positive Gaussian channel, possibly composed with a transposition.While a similar decomposition is shown to fail in the multi-mode scenario, we prove that it still holds at least under the further hypothesis of homogeneous action on the covariance matrix.1

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“…However, complications arise when dealing with mixed states, since there is no Hudson theorem for mixed states [54][55][56]. In particular there exist mixed states that are not mixtures of Gaussian states, yet have a positive Wigner function [57][58][59][60][61][62]. Despite this, we are going to introduce a computable resource quantifier based on the negativity of the Wigner function and we are going to show that it is a proper monotone for the resource theory at hand.…”

Section: Introductionmentioning

confidence: 99%

Resource theory of quantum non-Gaussianity and Wigner negativity

et al. 2018

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We develop a resource theory for continuous-variable systems grounded on operations routinely available within current quantum technologies. In particular, the set of free operations is convex and includes quadratic transformations and conditional coarse-grained measurements. The present theory lends itself to quantify both quantum non-Gaussianity and Wigner negativity as resources, depending on the choice of the free-state seti.e., the convex hull of Gaussian states or the states with positive Wigner function, respectively. After showing that the theory admits no maximally resourceful state, we define a computable resource monotone -the Wigner logarithmic negativity. We use the latter to assess the resource content of experimentally relevant states -e.g., photon-added, photon-subtracted, cubic-phase, and cat states -and to find optimal working points of some resource concentration protocols. We envisage applications of this framework to sub-universal and universal quantum information processing over continuous variables. * francesco.albarelli@unimi.it † marco.genoni@fisica.unimi.it ‡ matteo.paris@fisica.unimi.it § a.ferraro@qub.ac.uk arXiv:1804.05763v2 [quant-ph] 4 Dec 2018 1. M(ρ) = 0 ∀ρ ∈ G (resp. W + ).

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Detecting quantum non-Gaussianity of noisy Schrödinger cat states

Cited by 5 publications

References 14 publications

Direct detection of quantum non-Gaussian light from a dispersively coupled single atom

Direct detection of quantum non-Gaussian light from a dispersively coupled single atom

Normal form decomposition for Gaussian-to-Gaussian superoperators

Resource theory of quantum non-Gaussianity and Wigner negativity

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